The ever increasing demand for low-cost, low-complexity yet high-reliability transmission media in high-speed data communication devices results in a heavy reliance on copper/FR4 backplanes in serial data links. Consequently, transmission systems need to compensate for significant frequency-dependent channel losses that result from skin effect and dielectric loss in the copper traces and impedance discontinuities at the board/connector interfaces.
To equalize the channel loss in receivers operating at relatively low, i.e. less than 1 Gb/s, data transmission speed equalization of channel losses is performed in the digital domain using Finite Impulse Response (FIR) filters.
However, for receivers operating at high, i.e. multi-Gb/s, data transmission rates analog to digital converters (ADC) with sufficient speed and resolution are difficult to implement. Moreover, power consumption for such high speed ADCs and digital signal processors (DSP) can become prohibitive. Thus, equalization is more efficiently performed in the analog domain.
Analog FIR filters are continuous-time implementations of FIR filters and have gained popularity in applications that make use of higher data transmission rates as an alternative to conventional zero/pole peaking circuits, mainly because of their superior flexibility.
At data transmission rates beyond 10 Gb/s it becomes difficult to implement the delay elements in the AFIR filter because the delays required are on the order of intrinsic circuit propagation delays. For this reason distributed techniques are employed, using the propagation delays of on-chip transmission line sections that offer the additional advantage of being able to absorb circuit parasitics with inductive elements, thus extending the achievable circuit bandwidth.
The time-domain response of a 3-tap AFIR filter is given by the equation:Vo(t)=Vi(t)·a1+Vi(t−τ)·a2+Vi(t−2τ)·a3  (1)
Where,
                              a          k                =                              g            k                    ⁢                      R            2                                              (        2        )            
τ represents the time delay in the delay elements of the circuit;
Vo represents the output signal;
Vi represents the input signal;
t represents time; and
ak represents the FIR coefficients as implemented by amplifiers.
FIG. 1 illustrates a conventional 3-tap implementation for an AFIR filter 150 with three taps connected by four transmission line sections and two termination resistors. Note that the resistance value of the input termination resistor 121 and the output termination resistor 122 are each chosen to match the characteristic impedance of their respective transmission lines. The input transmission line comprises transmission line sections 141 and 142. The output transmission line comprises transmission line sections 143 and 144. Although the input and output transmission lines can have different characteristic impedances, for the sake of simplicity it is assumed here that they are both equal to R. Those skilled in the art can easily apply the following description to the case where input and output lines are used that have different characteristic impedances. The first tap 131 comprises a transconductance amplifier with gain g1 171. The second tap 132 comprises a transconductance amplifier with gain g2 172. The third tap 133 comprises a transconductance amplifier with gain g3 173. The first tap is connected to the second tap via transmission lines 141 and 143. The third tap is connected to the second tap via transmission lines 142 and 144. Each of the connecting transmission lines has a propagation delay that can be characterized by τ/2. This causes a phase shift in the analog signal.
FIG. 1 also illustrates the signal paths that occur in a conventionally tuned 3-tap AFIR filter 150. Assuming ideal transconductance amplifiers and transmission line sections, the time domain-response of the AFIR filter is represented by equation (1),Vo(t)=Vi(t)·a1+Vi(t−τ)·a2+Vi(t−2τ)·a3 with ak=gkR/2.FIG. 1 illustrates how this time-domain equation is generated. When there is perfect continuity in the channels (i.e. no impedance mismatch in the circuit), the signal travels along three paths. The first signal path 101 passes through the first tap 131 of the filter 150. This results in the first term of the time-domain equation Vi(t)·a1, where a1=g1R/2. The second signal path 102 passes through the second tap 132 of the filter 150. Because this second signal path 102 passes through two delay sections, the signal is delayed by 2×(τ/2)=τ. Thus the second term of the time-domain equation, Vi(t−τ)·a2, is generated, where a2=g2R/2. The third signal path 103 passes through the third tap 133 of the filter 150. Because this third signal path 103 passes through four delay sections, the signal is delayed by 4×(τ/2)=2τ. Thus the third term of the time-domain equation, Vi(t−2τ)·a3, is generated, where a3=g3R/2. Thus, in a conventional AFIR filter, the number of taps in the circuit corresponds with the number of polynomial terms in the time-domain response equation.
For applications operating at ultra-high data transmission rates (20-40 Gb/s) a distributed approach is a viable option for implementation of the AFIR equalizer. A problem arises however, when these high transmission systems need to be compatible with lower data transmission rates. At intermediate data transmission rates (10-20 Gb/s) the required tap delays are longer. One way to impose a longer tap delay is to lengthen the transmission lines. However, doing so takes up a lot of space during on-chip implementations of the filter.
Improvements in AFIR equalizers are desirable.